Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back


Surface Area and Volume of Combination of Solids

Have a doubt? Clear it now.
live_help Have a doubt, Ask our Expert Ask Now
format_list_bulleted Take this Lesson Test Start Test

Surface Area and Volume of Combination of Solids - Lesson Summary

Curved surface area (CSA) is the area of the curved surfaces for the solid. The remaining surfaces of the solid are the flat or the non-curved surfaces.

In a cone, the flat surface is the circular area of the base. In a cylinder, the flat surfaces are the top and bottom circular areas. A sphere has no flat surface, whereas a cuboid and a cube have only flat surfaces.

The flat surface area and the CSA of a solid together add up to the total surface area (TSA) for the solid.

Total Surface Area (TSA) = Curved Surface Area (CSA) + Areas of Flat Surfaces.

Diagonal of a cuboid = l 2 +  b 2 +  h 2 where l = length, b = breadth, h = height.

Diagonal of a cube = √3×a where a is side of a cube.

Area of a four walls of a room = 2(l + b)h where l = length, b = breadth, h = height.

Hollow cylinder
Let R and r be the external an internal radii of a hollow cylinder, and h be the height.

1) Thickness of Cylinder = R - r

2) Area of a cross section = π(R 2 - r 2)

3) External curved surface area = 2πRh

4) Internal curved surface area = 2πrh

5) Total surface area of a cylinder (TSA) = External curved surface area + Internal curved surface area + Area of two ends.
                                                          = 2πRh + 2πrh + 2π(R 2 - r 2)  = 2π( Rh + rh + R 2 - r 2 )

6) Volume of the material = πR2h - πr2h = π(R2 - r2)h.

A simple approach used for calculating the surface area and volume for complex shapes is split up the complex solid shapes into fundamental solid shapes. Apply the standard formulae to the fundamental shapes to calculate areas or volumes and add the results of the calculation.


Feel the LearnNext Experience on App

Download app, watch sample animated video lessons and get a free trial.

Desktop Download Now
Try LearnNext at home

Get a free home demo. Book an appointment now!